In this main section of the paper the simulation results of the different
parameter groups shall be discussed, starting with a comparison of the rotor,
including the nacelle with the isolated rotor, and subsequently analyzing
specific geometric variations, such as relative nacelle thickness, blade position
and junction shape.
General effects of the voluminous nacelle
To investigate the general effects of the nacelle on the blade root
aerodynamics, the cases CaseIsoRotor and
CaseT1.0 are compared. The flow field will be characterized,
and relevant coherent structures, three-dimensional effects and stall will
be addressed. A digression will be made on the challenges of
determining the AoA in the root region before the effect of the nacelle on
the aerodynamic coefficients is summarized.
Influence of the grid resolution on the sectional driving force.
Standard medium mesh (dashed), refined grid
(solid).
Vortices in the root area visualized by a Λ2 iso-surface
for CaseIsoRotor (a) and
CaseT1.0 (b). The vortices are colored by vorticity
in the y direction. The x=0 slice shows the normalized axial velocity
component.
Vortical structures
A first impression of the flow field can be gained by visualizing the
dominant vortical structures using the Λ2 criterion and the
axial velocity distribution in the center cut, as shown in
Fig. . For CaseIsoRotor the typical root
vortices emerge from balancing the bound circulation at the root. The contour
color of the iso-surface denotes the vorticity in the y direction and indicates
the expected sense of rotation. The normalized axial velocity u/U∞ in
the slice shows a distinct jet through the hub, which is responsible for the
relatively high advance rates of the root vortices. Apart from those, no
other relevant vortical structures are present that might indicate, e.g., flow
separation. Turning to CaseT1.0, shallow flow separation is
visible on the suction side near the junction with the nacelle. Moreover, the
dominant root vortex seen before has vanished. As will be discussed in more
detail in Sect. , the vortices spiraling around the
nacelle evolve from the two vortex legs of the HSV generated in the
blade–nacelle junction. As the convecting velocity is significantly smaller
than in CaseIsoRotor, these vortices, which are
counter-rotating, come very close to each other until eventually mutual
interaction occurs. This results in the formation of three-dimensional
turbulent structures in the wake of the nacelle. The application of eddy-resolving simulation techniques such as DES could bring further insight into
these interaction phenomena .
An effect that could be identified to enhance the generation of turbulent
structures in the nacelle wake is the consideration of both the rotating
spinner and the steady rear part of the nacelle. In previous simulations
during the project, in which the entire nacelle had been rotated, these
structures were almost absent . In order to
elaborate the effects of the boundary layer roll-up and detachment in the
rear part of the nacelle, isolated simulations of only the spinner and the
static rear part of the nacelle have been conducted. The vorticity in
the stream-wise direction evaluated in the inertial frame of reference is shown
in Fig. . The spinner is rotating in positive
convention around the x axis and accelerates the surrounding fluid that has
no circumferential component far off the wall and therefore generates a
negative x vorticity above the spinner. At the interface to the
nonrotating part of the nacelle this accelerated layer is suddenly retarded
again, inducing a positive x vorticity in the near-wall region above the
static surface. This results in a growing shear layer with positive
circumferential velocity that eventually detaches from the surface and forms
spiraling longitudinal vortices.
Turning to the mid-portion of the wake, a wavy velocity distribution can be
observed for both cases at around r/R=0.3. It is dedicated to trailed
vorticity associated with the span-wise gradients of bound circulation.
However, its strength appears to be significantly lower compared to the
vorticity directly at the root.
Vorticity in the stream-wise direction in the boundary layer of an
isolated nacelle including only the spinner and the static rear
part.
Three-dimensional flow and separation in the root region
The extent of the flow separation and three-dimensional flow patterns
can be retrieved from the surface streamlines on the suction side of the
blade shown in Fig. . For
CaseIsoRotor there is no flow separation at the root. The
slight radial flow component is dictated by the root vortex rolling from the
pressure to the suction side. This is also reflected in the velocity contours
in a slice x=2 m just cutting the leading edge of the blade. The
plotted velocity contours indicate the deviation velocity w̃
describing the vertical motion relative to the ideal circular path. Negative
values such as for CaseIsoRotor mean that the streamlines stem
from further outboard than assumed from kinematics.
By including the nacelle, its displacement effect evokes an effective
inclination angle in that plane, which results in a positive deviation
component w̃. For the inner 20 % of the rotor it is more than
0.5 m s-1. The negative values at around r/R=0.3 are subject to the
induction of the mid-trailing vortex described in the previous section. At
the inboard sections, a clear flow separation evolves from the junction with
the nacelle. It spreads in the radial direction and realigns with the chord direction
at about r/R=0.17. When focusing on the pressure contours, they are mostly
parallel for CaseIsoRotor except for the very inboard region
that is directly influenced by the root vortex. For CaseT1.0
significant curvature of the isobars is visible in the area covered by the
dividing streamline. As part of the separation process it can be observed
that the angle of the shear stress vector turns relative to the pressure
gradient, indicating a complex interaction of centrifugal, Coriolis and
pressure forces as drivers of the three-dimensional flow. Due to the very
high solidity of the blade, which varies between c/r≈1.1 at
r/R=0.1 and c/r≈0.5 at r/R=0.2, a high impact of three-dimensional effects can be expected.
Visualization of three-dimensional flow in the root region using
streamlines and pressure contours on the suction side of the blade for
CaseIsoRotor (a) and
CaseT1.0 (b). The contour lines indicate the
“deviation velocity” w̃ from the ideal kinematic value -Ωy in a slice at x=2 m.
To estimate the share of these forces acting in the y–z plane, the simple
balance can be written for a rotation around the x axis as
0=-∂p∂y∂p∂z+ρΩ2yΩ2z+ρ2Ωw-2Ωv,
where the second and third term denote the centrifugal and Coriolis forces,
respectively. The velocity components v and w are acting in the chord- and
span-wise direction relative to the moving blade rotating with Ω. As
can be directly seen in the equation, by definition the Coriolis force
vanishes when the velocity is tangential to the rotation, and hence it is
expected to be small directly above the nacelle. For the balance in the span-wise
direction the Coriolis force changes sign with respect to the chord-wise
velocity component, acting inward for attached flow, outward for separated
flow and particularly vanishing near the dividing streamline. In contrast to
that, the centrifugal force component in the span-wise direction is simply
proportional to the z coordinate. Therefore, at the point of separation,
the only force to hold the fluid particle on the path of rotation would be a
span-wise pressure gradient dp/dz. The latter can be
derived from the radial pressure distribution plotted in
Fig. for different chord-wise sections. At
xc/c≈0.5, which is close to the separation point, there is
virtually no span-wise pressure gradient. Hence, the fluid moves outward
solely due to the centrifugal force. It would accelerate towards the tip due
to the increasing centrifugal force with z if there was no Coriolis force.
As the outward movement is naturally connected with a positive w component
it deflects the flow in the chord-wise direction and once there is a chord-wise
component and a positive v velocity, an additional inward deflection is
induced until eventually the flow realigns with the chord direction. The
transport of separated fluid in the outward direction is known as centrifugal
pumping and also allows for a pressure
recovery in the radial direction, whereby the adverse pressure gradient is
smaller compared to the chord-wise direction (see, e.g., xc/c≈0.85 in Fig. ). For equivalent
two-dimensional conditions, most of the pressure recovery would therefore
occur in the turbulent mixing of the airfoil wake. This explains the commonly
observed stall delay of a rotating blade compared to equivalent
two-dimensional conditions (e.g.,
).
The effect of the nacelle on radial pressure distribution on the
suction side at xc/c≈0.1 (squares), xc/c≈0.5 (triangles) and xc/c≈0.85 (circles) for
CaseIsoRotor (dashed), CaseT1.0
(solid)
The current investigation supports the studies
of , and
recently , who explained radial flow with
centrifugal force as well. In this study, the significantly higher blade
solidity caused by the flat-back airfoils with large chord is seen to be
responsible for a significant impact of three-dimensional effects.
Turning to the front part of the blade, it can be shown that following
Bernoulli's principle, the static pressure decreases in the radial direction due
to the increasing dynamic pressure of the inflow. This results in an outward
pressure gradient. However, it is not believed to be the only reason for the
slight radial component of the streamlines near the leading edge, since
the pressure gradient is balanced by the Coriolis force in the negative
z direction and a strong acceleration in the chord-wise direction
prevails, which is in accordance with . As
described in more detail in Sect. it is more related
to an effective sweep angle of the blade relative to the inflow direction.
This is again an effect of the high solidity of the blade, which results in
a leading edge shift relative to the rotational axis in the y direction. Comparing
the pressure levels, the suction peak is significantly reduced in
CaseIsoRotor due the induction of the root vortex over the
whole inner portion of the rotor.
Determination of the angle of attack in the root region
In order to assess the aerodynamic performance of the individual blade
sections in terms of aerodynamic coefficients and to utilize that information
in two-dimensional approaches such as BEM or for airfoil design tools, it is
essential to accurately determine the angle of attack (AoA) from the
three-dimensional flow field. However, it is clear that its extraction is far
from trivial as wind velocity and rotation are superimposed by the induction
of the wake and the bound circulation of the blade itself. Most approaches
such as those compared by aim to eliminate the
effect of bound circulation. They provide very similar results at the
mid-board blade sections. However, at the blade tip and root, major
differences were observed. For the root region they were explained by the
massive flow separation in the wake of the very thick airfoils. As for the
present rotor, flow separation is only shallow or even absent, differences
between the AoA extraction methods are strongly linked to the effects of the
root vortex system instead of the dominant vortex shedding caused by massive
flow separation. Therefore, two AoA evaluation methods shall be compared with
a focus on the root region.
Extraction of axial velocity in the inertial frame near the tip and
the root using the reduced axial velocity
method (circular arcs) and the line
average (closed curves)
method.
Radial distribution of the angle of attack for
CaseIsoRotor (dashed) and CaseT1.0 (solid)
using the RAV method (gray) and the line average method
(colored).
The first is the reduced axial velocity (RAV) method
of , which eliminates bound circulation by
azimuthally averaging the axial velocity for each radial section. Secondly,
the line average method of is applied,
which averages the velocity vector along closed lines around the blade. Both
methods are sketched in Fig. . As seen in the figure,
for the line average method, the extraction of the velocities occurs
along circles that are curved about the rotational axis with a radius
corresponding to the location of the quarter-chord point in each section,
being centered around the latter. The radius of the projected circle is one
chord length. By averaging the planar velocity vector along these curves,
could show that the effect of bound circulation
can be eliminated, resulting in pure inflow conditions for that section.
The evaluation of the AoA in Fig. shows a lower AoA
near the tip for the line average method, since it locally accounts
for the induction of the tip vortex, which is smeared out by the azimuthal
averaging in the RAV method (Fig. ). Accounting for
the local induction is a desired feature of the line average method
and has been shown to accurately reconstruct inflow conditions for
corresponding two-dimensional analyses of the near-tip region
(; ). Near the
blade root, the AoA predicted by the line average method is higher
than obtained by the RAV method. The reason for this is that the azimuthal
arc length for averaging the axial velocity in the RAV method is now smaller
compared to averaging over the circular line of the line average
method (Fig. ). Particularly, the acceleration of
the curving streamlines upstream of the airfoil is not considered in the RAV
method. This effect becomes particularly important
for CaseT1.0, for which both the blade and the nacelle displace
the flow and therefore accelerate it upstream of the leading edge, which is
the reason why the increase in AoA is more pronounced for the case including
the nacelle. Additionally, it must be noted that for the RAV method the root
vortex is occupying about 40 % of the downstream arc length, being more
concentrated for the line average method. As a consequence the
latter predicts a higher axial velocity in the rotor plane compared to the
RAV method (Fig. ) and therefore a higher AoA.
In the remainder of the paper, the AoA will be evaluated with the
line average method.
Radial distribution of the axial inflow velocity for
CaseIsoRotor (dashed) and CaseT1.0 (solid)
using the RAV method (gray) and the line average method
(colored).
The effect of the nacelle on aerodynamic coefficients
The pressure coefficient Cp is compared for the configurations
CaseIsoRotor and CaseT1.0 as well as
two-dimensional airfoil simulations in a slice at r/R=0.136
(Fig. ). Following Bernoulli's principle, the pressure
coefficient has been normalized using the maximum dynamic pressure that can
be exploited from the kinematics q∞,rot=ρ/2U∞2+(Ωr)2. In accordance with the
independence principle of swept-wing theory, only the component normal to the
leading edge is relevant for the aerodynamic properties. Therefore, the
z coordinate has been used as the radius for the circumferential component in
the dynamic pressure. It should be noted that one could also account for the
induction and sweep angle effects, but then the reference state becomes
rather ambiguous and difficult to compare among the different cases. Hence,
it will be accepted that with the kinematic normalization, Cp might differ
from a value of 1 in the stagnation point and it will be attempted to
explain this with dominant physical effects.
As already discussed in the previous section, the induction of the root
vortex significantly diminishes the suction peak for
CaseIsoRotor. For the rotor including the nacelle, the
pressure level is lower for the entire suction side of the blade,
particularly in the front part of the airfoil. Hence higher lift and lower
pressure drag can be expected for CaseT1.0. At the pressure
side the differences are small. Only directly at the stagnation point is a
higher pressure coefficient obtained by CaseIsoRotor,
which is slightly >1. This can be explained by the negative w̃
contours (Fig. ), which indicate that the fluid
hitting the airfoil is actually stemming from further outboard compared to
its ideal kinematic path. Therefore, fluid of higher momentum is transported
towards the leading edge of the airfoil, yielding a higher stagnation
pressure than assumed for normalization. By contrast, in
CaseT1.0 the stagnation pressure is lower than estimated due
to an effective inclination angle that pushes fluid from the inboard
sections to the reference cut. Finally, focusing on the aft chord region, it
can be confirmed that also for CaseT1.0 the cut is outside of
recirculation and that pressure has almost recovered by the centrifugal
pumping mechanism.
To further assess the three-dimensionality of the flow in the hub region, a
comparison shall be drawn with two-dimensional simulations. These were
performed at angles of attack α=10.2, 13 and
14∘, at which the first corresponds to the extracted value from the
RAV method for CaseT1.0, the second corresponds to a slightly
higher value than obtained from the line average method, which was
12.3∘ for CaseT1.0, and the last is close to the AoA
obtained for increased nacelle thicknesses as shown in
Sec. . The 2-D results at α=10.2∘
reveal no separation. At α=13∘ shallow trailing edge
separation is present, which moves forward to xc/c≈0.6 at
α=14∘. Compared to the 3-D results,
CaseIsoRotor shows a completely different behavior that
cannot be mimicked by any 2-D simulation. At first glance the level of the
suction peak of CaseT1.0 suggests that
α=10.2∘ would be a good approximation. However, it must be
pointed out that when scaling the stagnation pressure in the 3-D results to a
value of 1, the distribution increases a bit. Moreover, the visual
inspection of corresponding streamline plots compared in that section (not
shown here) clearly suggested a larger AoA than 10∘. The
distribution in the adverse pressure regime is very similar to the 2-D
results at α=13∘, implying a similar boundary layer stress. The
differences on the pressure side are also marked, showing distinctly
stronger suction peaks predicted by the two-dimensional simulations.
These examinations emphasize the strong three-dimensionality of the flow in
the root region of the present rotor and point out that the application of
two-dimensional polars in BEM without correction models must be treated with
caution, even if there is no massive flow separation.
Pressure coefficient Cp at r/R=0.136 for
CaseIsoRotor (solid red) and CaseT1.0 (solid
blue) compared with two-dimensional simulations (gray lines):
α=10.2∘ (solid), α=13∘ (dashed), α=14∘
(dashed dot).
Distribution of aerodynamic coefficients along the blade radius for
CaseIsoRotor (dashed) and CaseT1.0
(solid).
Visualization of three-dimensional flow in the root region using
streamlines and pressure contours for CaseT1.0 (a),
CaseT1.2 (b) and
CaseT1.4 (c). The contour lines are plotted for a
slice at x=2 m and indicate the velocity w̃=w-Ωy,
which denotes the deviation from the ideal kinematic
path.
The radial distribution of the circulation Γ plotted in
Fig. a and the lift coefficient
(Fig. b) confirm the improvement of the aerodynamics
in the root region by including the nacelle, which effectively diminishes the
harmful inductive effect of the root vortex. This is also reflected in a
reduction of the drag coefficient (Fig. c) by up to
100 drag counts, although CaseT1.0 involves flow separation.
The region of influence of the nacelle extends to r/R=0.35. By integrating
the driving force within that range, this results in a higher torque of
around 20 % for that portion.
The impact of the relative nacelle thickness
From the previous section it was concluded that an improvement of the
aerodynamic properties in the inner portion of the rotor could be obtained by
taking into account the nacelle. The attenuation of the root vortex by the
nacelle diminished induced drag and increased lift. In this section the
effects of the relative nacelle thickness will be analyzed. The thickness has
been increased in two steps by a factor of 1.2 and 1.4
for CaseT1.2 and CaseT1.4, respectively.
The effect on flow separation and its driving parameters
The resulting surface streamlines and pressure contours shown in
Fig. indicate growing flow separation with
increasing nacelle thickness. The extent of the separation measured from the
point of maximum thickness of the nacelle to the radial position of
reattachment increases from 0.08R over 0.10R to 0.12R for the
configurations CaseT1.0, CaseT1.2 and
CaseT1.4, respectively. With increasing thickness of the
nacelle the separation line moves forward by around 15 %. In addition, it
can be noted from the “deviation velocity” w̃ that the inclination
of the inflow increases with larger relative nacelle thickness.
Airfoil pressure distribution at r/R=0.136 for
CaseT1.0 (solid), CaseT1.2 (dashed),
CaseT1.4 (dashed dot) and CaseT1.4-twistmod
(dashed dot dot). The gray curves denote corresponding inviscid
simulations.
The comparison of the pressure coefficient in the reference cut at
r/R=0.136 (Fig. ) confirms the increasing separation
for larger nacelle thicknesses. The distinct pressure plateau already
suggests a loss of aerodynamic efficiency due to flow separation. The radial
pressure gradients in the front part of the blade
(Fig. ) show that greater relative nacelle
thickness increases the suction force due to the displacement effect of the
nacelle. Also, in the mid-chord and aft chord region the initial pressure level
is lower, which increases the radial adverse pressure gradient. Since
separation inherently alters the pressure distribution, it is difficult to
distinguish between the causes and effects of flow separation. In order
to assess whether stronger adverse pressure gradients develop by increasing
the nacelle thickness, inviscid reference simulations have been performed for
CaseT1.0 and CaseT1.4. The interaction of the
inviscid pressure fields is visualized in Fig.
using vectors of static pressure acting on the surfaces. For
CaseT1.0 the flow accelerates moderately in the junction,
reaching the minimum of pressure at about xc/c≈0.5–0.6.
It can be shown that the adverse pressure gradient imposed by the nacelle is
slightly shifted behind the one from the blade. Turning to
CaseT1.4 this is no longer the case, as the suction peaks
fairly coincide at around xc/c≈0.3–0.4. Downstream of
that point the adverse pressure gradient markedly increases compared to
CaseT1.0 and is accordingly devolved on the blade as shown in
Fig. . In CaseT1.0 the inviscid and
viscous suction peaks closely coincide, whereas a significantly higher peak
prevails for the inviscid simulation of CaseT1.4. This
clearly suggests that the boundary layer of the associated viscous case is
increasingly loaded with larger nacelle thickness. From these investigations
it can be concluded that a reduction of separation might be achieved by
decoupling the interfering pressure gradients of the nacelle and the blade, as
is typically done for winglets.
A second aspect that turned out to be crucial for the development of the
flow separation is directly linked to the vortex system evolving in the
junction of the blade and the nacelle. The motivation for a detailed look
into that came by analyzing AoA behavior with respect to the
different nacelle geometries (Fig. ), for which an
increasing AoA of around 2∘ could be observed from
CaseT1.0 to CaseT1.4. In the beginning of the
investigations, it was assumed that the increasing separation was the primary
effect of the larger AoA. Therefore, it was attempted to redesign the blade
in order to compensate for the AoA, leading to
CaseT1.4-twistMod,
which employs an increased twist angle in the blade root region of around
2.0∘ (see Fig. ). Except for the sections very close
to the root, the AoA could be effectively reduced. Very inboard, the
aerodynamic behavior is obviously strongly nonlinear. Due to the twist
modification the flow is redirected, which causes an increase in the axial
velocity. The latter is detected by the line average method, which
evaluates a lower AoA reduction than expected by the geometric twist
modifications. In turn the RAV method was closer to the kinematic value.
Nevertheless, when looking at the pressure distribution in
Fig. , the suction peak is significantly reduced. The
evaluation of chord-wise skin friction (Fig. ) shows
that the separation remains almost the same as for CaseT1.4,
so it could be concluded that flow separation is not directly affected by an
AoA-induced adverse pressure gradient on the blade.
Airfoil skin friction distribution at r/R=0.136 for
CaseT1.0 (solid), CaseT1.2 (dashed),
CaseT1.4 (dashed dot) and CaseT1.4-twistmod
(dashed dot dot).
It is seen to depend more on the interacting boundary layers in the junction
region of the blade and the nacelle. To shed more light on that, the
emerging vortices in the junction are visualized in
Fig. for CaseT1.0 and
CaseT1.4 using volume streamlines colored by vorticity in the
local direction of the velocity vector. Additionally, volume cuts are placed
normal to the blade at the leading edge and at
xc/c=[0.25;0.5;0.75]. The horseshoe vortex (HSV)
is clearly visible and seems to be generated in the stagnation region when
the boundary layer of the nacelle approaches the blade. It is rolling inward
and its size and strength could be observed to increase with larger nacelle
thickness. This behavior is consistent with , who
reports a stronger HSV with increasing AoA.
showed experimentally that the onset of corner separation is delayed by a
stronger HSV, since fluid of higher momentum is pushed into the blade
boundary layer. This beneficial inductive effect likewise depends on the
distance to the blade. By increasing AoA the suction side leg departs from
the blade and is further deflected by the Coriolis force.
Inviscid pressure distribution in the junction region of the blade and
nacelle for CaseT1.0 (a) and
CaseT1.4 (b).
Directly inboard of the HSV, the counter-rotating corner vortex (CV) evolves
from the stagnation point and closely follows the juncture of the blade and
the nacelle. Its production depends on the velocity gradients of the
interacting boundary layers and its strength was observed to increase for the
larger relative nacelle thickness in the adverse pressure gradient region. In
contrast to the HSV, the CV remains aligned with the junction. Due to its
sense of rotation it seems to be responsible for deforming the near-wall velocity
profile on the blade and pulling the boundary layer flow away from the wall.
For all cases it was observed that the recirculation area was initiated from
the streamline originating in the CV. Thus, high vorticity in the CV might be
an important driver for the whole separation process. In particular it should
be noted that the configuration with modified blade twist
(CaseT1.4-twistMod) revealed quasi-identical values for the
CV strength as CaseT1.4 and showed the same amount of
separation.
Hence, the second strategy to diminish the detrimental flow separation could
be a relief of the mutual loading of the boundary layers of the blade and
the nacelle in order to influence the CV strength and propagation. This
aspect shall be investigated in Sect. .
Vortex system in the junction of the blade and nacelle for
CaseT1.0 (a) and
CaseT1.4 (b).
The effect of the relative nacelle thickness on aerodynamic coefficients
To summarize the effects of relative nacelle thickness on the aerodynamic
coefficients in the root region, which are plotted in
Fig. , they confirm the degradation of
aerodynamic performance due to stronger flow separation in the inboard
region where lift mostly decreases and particularly drag increases. The AoA
increases with nacelle thickness, since reduced lift decreases axial
induction, which yields higher axial velocities in the rotor plane. The
decrease in aerodynamic efficiency is most prominent for the inner 25 %
of the rotor radius. It should be noted that there was no measurable benefit
for the outer rotor sections as one might have expected due to a displacement
effect of the nacelle. In total, the torque generated by one blade decreased
for CaseT1.4 by 1.18 % compared to
CaseT1.0.
Movement of the blade position relative to the
nacelle
As pointed out in Sect. , a segregation of the
interacting pressure gradients of the blade and the nacelle could reduce the
overall loading on the corner boundary layer. In order to analyze these
effects, the blade was shifted upstream in the axial direction
(CaseT1.4-dXm04), as well as upstream and downstream in
the circumferential direction (CaseT1.4-dYm05 and
CaseT1.4-dYp05, respectively). All modifications were based
on the nacelle with the largest of the considered thicknesses, since
the strongest effects on the flow separation might be present there and
this configuration provides more space for relative blade shifts.
The motivation for the first modification was to place the entire blade in
front of the point of maximum thickness of the nacelle and therefore locate
it in the favorable pressure gradient in the axial direction. The shifting of the
blade in the y direction correspondingly aims to investigate the relative
location of the pressure gradients in the circumferential direction.
investigated the lateral shift of rotating profiles
for the first time and focused on the exploitation of the y component of
the centrifugal force in Eq. () to increase rotor
performance.
The effect of the nacelle thickness on radial pressure
distribution on the suction side at xc/c≈0.1 (squares),
xc/c≈0.5 (triangles) and xc/c≈0.85
(circles) for CaseIsoRotor (dashed), CaseT1.0
(solid), CaseT1.4 (dashed
dot).
Aerodynamic coefficients along the blade radius for
CaseT1.0 (solid), CaseT1.2 (dashed),
CaseT1.4 (dashed dot) and CaseT1.4-twistmod
(dashed dot dot).
The effect of the relative blade position on flow separation
Comparing the surface streamlines plotted in
Fig. with those of the centered version
(Fig. ), the movement of the blade forward in
the axial direction reveals no improvement regarding the extension of the corner
separation. Indeed, even a slight deterioration is present, which might be
caused by the fact that the inclination angle relative to the blade
increases. Turning to CaseT1.4-dYp05, an increase in the
separation extent by around 8 % can be observed compared to
CaseT1.4. Here, separation already begins close behind
30 % of chord. A significant improvement can be achieved by shifting the
blade in the direction of rotation. The separation size in the radial direction is
0.086R, which is only slightly above the baseline CaseT1.0
but already smaller than in CaseT1.2.
Visualization of three-dimensional flow in the root region using
streamlines and pressure contours for
CaseT1.4-dXm04 (a),
CaseT1.4-dYm05 (b) and
CaseT1.4-dYp05 (c). The contour lines are plotted
for a slice at x=2 m (x=1.5 m for
CaseT1.4-dXm04) and indicate the velocity w̃=w-Ωy, which denotes the deviation from the ideal kinematic
path.
The boundary layer profiles in the reference cut r/R=0.136
(Fig. ) give information about the mass flow rate of
recirculation. At xc/c=0.5, CaseT1.4-dYm05 is
still attached, whereas slight and moderate backflow is observed in
CaseT1.4 and CaseT1.4-dYp05, respectively.
Turning to the profiles at xc/c=0.75, the height of separation
massively increases when shifting the blade in the positive y direction. As
seen in Fig. this seems to be linked with the
volume covered by the downward curvature after the point of maximum thickness
of the nacelle and might be “felt” by the blade boundary layer as an
additional expansion, which goes along with added adverse pressure loading.
This effect is weaker for CaseT1.4-dYm05, for which most of the
pressure recovery is achieved forward of that point.
In a similar way, the chord-wise (Fig. ) pressure
distributions are affected in accordance with previous observations. In
CaseT1.4-dXm04, the suction peak decreases, but the kink to
the pressure plateau remains at the same position as for
CaseT1.4. In the aft chord region the pressure recovery has
still not initiated as it might be “blocked” by the displacement effect of
the ascending nacelle diameter in the vicinity of the blade suction side. In
CaseT1.4-dYp05, the massive flow separation yields a collapse
of lift at xc/c≈0.4, which results in a reduced suction
peak. Both cause a tremendous increase in pressure drag. The latter can
certainly be reduced for CaseT1.4-dYm05, for which moderate
separation begins at xc/c≈0.65. The downward slope shows
that the last part of the pressure recovery already occurs along the airfoil
and not predominantly in the wake, as for the other cases.
Regarding the span-wise pressure distribution
(Fig. ), a slight increase in suction force can
be noted near the leading edge in CaseT1.4-dYm05 for the
whole inner portion, whereas it is markedly lower when moving the blade in
the other direction. In contrast to the other cases,
CaseT1.4-dYm05 maintains the slope of the leading edge cut,
also along xc/c=0.5. Particularly, CaseT1.4-dYp05
already shows the behavior typically found near the trailing edge, where
pressure recovery is redeployed in the radial direction by the centrifugal
pumping mechanism. Consistently at xc/c=0.85, the radial pressure
gradient is smallest in CaseT1.4-dYm05, since less
recirculating mass needs to be transported outward, which directly yields an
earlier realignment of the streamlines in the chord-wise direction as seen in
Fig. .
From the previous investigations in Sect. using the
Euler simulations, it became clear that a decoupling of the adverse pressure
gradients seems necessary to relieve the boundary layer in the junction. As
could be shown the axial shifting did not yield any improvement, so it
can be deduced that the predominant pressure gradient is the one in the lateral
direction. This also seems reasonable as the flow in the junction is aligned
with that direction. As the adverse pressure gradient imposed by the nacelle
initiates at the outmost point in the circumferential direction, it follows that
the entire pressure recovery is additionally loaded in
CaseT1.4-dY05. Opposed to that, the segregation of the
adverse pressure gradients seems to work for CaseT1.4-dYm05.
Another important aspect to be considered is already attributed to
inflow. As shown by the left sketch in Fig. ,
the inner sections of the blade that are shifted forward are affected by
inflow stemming from an effectively larger radius that consequently brings in
greater momentum. Along the airfoil the flow is pushed downward compared to
its ideal kinematic path, which means that it is effectively streaming from
a larger to smaller radius. According to the conservation of angular momentum this
results in acceleration, which is supportive in overcoming the adverse pressure
gradient. When crossing the x–z plane a corresponding retardation would
prevail, which additionally reduces angular velocity in
CaseT1.4-dYp05. To illustrate this inflow hypothesis, a
velocity difference plot between CaseT1.4-dYm05 and
CaseT1.4 is presented in Fig.
for the reference cut r/R=0.136. For this visualization, the solution of
CaseT1.4-dYm05 was mapped on top of the centered version. For
the entire front part of the airfoil a higher velocity magnitude prevails,
which is particularly present inside the boundary layer as seen in
Fig. . In the stagnation region the inflow velocity is
≈1m s-1 higher for CaseT1.4-dYm05 compared to
CaseT1.4. Another distinct peak at which the velocity is
markedly higher for CaseT1.4-dYm05 is found in the region of
adverse pressure at around xc/c≈0.5. In the rear part of
the airfoil the differences originate from the different thickness of the
separated wake.
The third effect that is seen to be beneficial for the delay of separation by
shifting the blade in the direction of rotation is the sweep angle of the inflow
vector with respect to the blade leading edge. At the reference cut it
comprises more than 25∘ for CaseT1.4-dYm05, about
17∘ for CaseT1.4 and around 9∘ for
CaseT1.4-dYp05. In the radial direction the sweep angle decreases
exponentially, but is still greater than 5∘ at the tip for
CaseT1.4-dYm05. As the flow turns about the airfoil, the
effective sweep angle is not constant along the chord-wise direction, but
since most of the lift is generated in the front portion of the blade, it can
certainly be stated that sweep effects cannot be neglected. This is supported
by the streamlines in CaseT1.4-dYm05
(Fig. ) that show the typical pattern found
for swept wings at high AoA , featuring a
distinct attachment line instead of a stagnation point, which results in
Cp,max<1 and a prominent span-wise deflection of the
streamlines near the trailing edge. In contrast to that, the streamlines
remain approximately perpendicular to the leading edge in
CaseT1.4-dYp05. The question of whether the principle of
independence holds or not is certainly debatable, since rotation introduces
span-wise gradients to the flow field. Indeed, for attached boundary layers
it is a typical assumption made in BEM codes and is also supported by
analyses of . At high AoA in the stall regime it
is generally no longer valid. However, as observed in the boundary layer
profiles (Fig. ), the streamlines
(Fig. ) and pressure distribution
(Fig. ), there is evidence that the sweep angle delays
stall and is beneficial for reattachment as it stimulates the outward
centrifugal pumping mechanism. An overview of the effect of sweep angle on
dynamic stall can be found in the text book
of . Measurements reinforcing the present
observations regarding the effect of sweep angle on maximum lift coefficient
and stall delay can be found, for example, in and
in .
Stream-wise normalized velocity in the boundary layer
u/U∞,rot at r/R=0.136 and
xc/c=[0.25;0.5;0.75] (squares; triangles; circles), for
CaseT1.4 (solid), CaseT1.4-dYm05 (dashed dot)
and CaseT1.4-dYp05 (dashed).
Airfoil pressure distribution at r/R=0.136 for
CaseT1.4 (solid), CaseT1.4-dXm04 (dashed dot
dot), CaseT1.4-dYm05 (dashed dot) and
CaseT1.4-dYp05 (dashed).
The effect of the blade position relative to the nacelle on aerodynamic coefficients
Regarding the global consequences of the relative blade position, they shall
be compared in terms of AoA, lift and drag coefficients plotted for the
inner rotor half in Fig. . The AoA seems to generally
increase when flow separation becomes stronger, which was already seen for the
cases in which the nacelle thickness had been increased. Compared to
CaseT1.4, the axial movement of the blade decreases
torque by 0.96 % as lift declines and drag slightly rises. The
significantly stronger flow separation in CaseT1.4dYp05
further deteriorates aerodynamic efficiency and is reflected in a decline of
torque by 1.98 %. CaseT1.4dYm05 clearly increases
lift and decreases drag in the inner portion of the rotor, which raises torque
by 2.1 %. This configuration is already better than
CaseT1.2, but still around 1.5 % worse than
CaseT1.0. However, as will be shown in the next section, a
movement of the blade in the direction of rotation based on
CaseT1.0 is able to outperform the aerodynamic behavior of
the latter.
The effect of the blade position on radial pressure distribution
on the suction side at xc/c≈0.1 (squares),
xc/c≈0.5 (triangles) and xc/c≈0.85
(circles) for CaseT1.4 (solid),
CaseT1.4-dYp05 (dashed), CaseT1.4-dYm05
(dashed dot).
Sketch of the shifted profiles at r/R=0.136 (a).
Difference in velocity magnitude between CaseT1.4-dYm05 and
CaseT1.4 (b).
Aerodynamic properties along the blade radius for
CaseT1.4 (solid), CaseT1.4-dXm04 (dashed dot
dot), CaseT1.4-dYm05 (dashed dot) and
CaseT1.4-dYp05 (dashed).
Visualization of three-dimensional flow in the root region using
streamlines and pressure contours for
CaseT1.0-rounded (a),
CaseT1.0-fairing (b) and
CaseT1.0-dYm05 (c). The contour lines indicate the
“deviation velocity” w̃ from to the ideal kinematic value -Ωy in a slice at x=2 m.
Fillet-type modifications in the junction
The second strategy for a potential reduction of corner separation elaborated
in Sect. was the relief of the boundary layer
interaction of blade and nacelle, which shall be addressed in this section.
The considered configurations modify the geometry of the junction by applying
a constant radius of 0.4 m all around the airfoil, denoted
CaseT1.0-rounded, and introducing a fairing on the suction
side of the blade referred to as CaseT1.0-fairing. These
modifications are based on CaseT1.0. Since the movement of
the blade in the direction of rotation showed promising results when based
on the largest nacelle, this modification shall be transferred to the
smallest nacelle (CaseT1.0-dYm05) and included for
comparison in the present discussion. In the rear part the junction reveals a
plateau, which is from another case not shown here ,
that
turned out to be beneficial regarding a restriction of the recirculation
area. Since the lateral shift on this nacelle brings along conflicts
regarding meshing when moving the blade forward, the periodic segment had to
be rotated by 17∘, but due to axisymmetry, this does not change
anything regarding periodicity.
The effect on flow separation and the corner vortex system
The streamline plot in Fig. shows that flow
separation can be entirely suppressed for CaseT1.0-dYm05 and
CaseT1.0-fairing. For the latter quasi-two-dimensional flow
conditions prevail with only slight streamline deflection close to the
trailing edge, whereas the shifted blade again shows the streamline patterns
of swept wings. In CaseT1.0-rounded, flow separation cannot
be noticeably reduced compared to CaseT1.0
(Fig. ).
Vortex system in the junction of blade and nacelle for
CaseT1.0-rounded (a) and
CaseT1.0-fairing (b).
More details on the separation mechanism (and suppression) can be gathered
from the vortex system shown in
Fig. . Although the footprint of the
surface streamlines indicates a similar separation size for
CaseT1.0-rounded compared to the baseline configuration with
sharp juncture, recapitulation of Fig.
confirms that the separation thickness decreased by introducing the rounding.
A side effect of the latter is a weakening of the production of the HSV in
the nose region achieved by a homogenization of the shear layer shown in the
foremost slice of the approaching nacelle boundary layer interacting with the
blade. Although a streamline that is counter-rotating to the HSV vortex
rotating can be identified in its vicinity, no harmful corner vortex can
build up and manifest itself in the junction. Separation is not initiated
from a distinct streamline, but evolves from an isolated vortex generated in
the transition from the rounding to the actual blade surface.
These findings were borne in mind in the design of
CaseT1.0-fairing. It was decided to reduce the fillet nose
radius to 0.2 m in order to increase the strength of the HSV again, which
is believed to be helpful for the reduction of corner
separation . This is certainly the conservative
approach, since the separation should optimally be suppressed in combination
with a reduced or even eliminated HSV, as the latter increases the
interference drag and is a source of noise
.
Towards the trailing edge, the local radius was increased on the suction side
to eliminate the unfavorable pressure rise induced by the shape in the
transition to the blade previously seen in CaseT1.0-rounded.
As can be observed in the streamlines and in the foremost slice
plotting the vorticity contours, the strength of the HSV could be increased
by a factor of 3. Its suction side leg remains closer to the blade, as it
is not displaced by any recirculation and is deformed ovally when traveling
downstream.
In the work of , the formation of the corner
vortex correlated well with a peak in the Reynolds shear stress generated by
chord-wise and span-wise velocity. In order to assess the development of
the corner vortex for CaseT1.0 and
CaseT1.0-fairing, the contours of the vw shear
stress are depicted in Fig. for a field slice cutting the
blade at xc/c=0.5. The plot confirms the peak and the change in
sign of shear stress for CaseT1.0, similarly as observed
in , and gives evidence for the production of
the corner vortex. In CaseT1.0-fairing, the large rounding
radius ensures a smooth mixing of the boundary layers, resulting in a
homogeneous distribution of shear stress that prevents the generation of the
CV. Additionally, as was already suggested by the streamline plot in
Fig. , the formation of the HSV is altered
as well. Its strength is lower than in CaseT1.0 and it is
stretched. The fact that its center is located significantly closer to the
blade surface is beneficial regarding its induction on the blade.
Reynolds shear stress vw of the chord-wise and
span-wise velocity at xc/c=0.5.
CaseT1.0 (a),
CaseT1.0-fairing (b).
Pressure coefficient at r/R=0.136. CaseT1.0
(solid), CaseT1.0-rounded (dashed),
CaseT1.0-fairing (dashed-dot), CaseT1.0-dYm05
(dashed dot dot).
Distribution of aerodynamic coefficients along the blade radius for
CaseT1.0 (solid), CaseT1.0-rounded (dashed),
CaseT1.0-fairing (dashed dot) and CaseT1.0-dYm05
(dashed dot dot).
The effect of fillets on the aerodynamic coefficients
Turning finally to the quantities related to aerodynamic efficiency, the
pressure distribution in Fig. clearly shows the
improvement obtained by eliminating the corner separation for
CaseT1.0-dYm05 and CaseT1.0-fairing. The
suction force is particularly larger between 40 and 60 % chord, and the
boundary layer is able to stand the adverse pressure gradient, which leads to
an effectively higher pressure value in the vicinity of the trailing edge.
The attached flow in the corner reduces the AoA
(Fig. c), consistent with previous observations,
being most pronounced for CaseT1.0-dYm05. As already
indicated by the pressure distribution in Fig. ,
CaseT1.0-fairing particularly increases lift and only
marginally decreases drag, whereas for CaseT1.0-dYm05 the
improvements are more related to drag. Overall, tangential force increases in
CaseT1.0-fairing due to greater lift. The evaluation of these
local improvements on the global blade performance is discussed in the next
section.
Comparison of the flow field in the root region for
CaseT1.0 and CaseT1.0-fairing at off-design
wind speeds: U∞=8, 12 and 15 m s-1. Surface
streamlines (column a) and chord-wise
velocity distribution at z/R=0.2 (column b).
Assessment of integral quantities and off-design conditions
As previously mentioned, it is important to put very local aerodynamic
improvements in a more global context by analyzing their impact on the
sectional thrust and driving loads of the entire blade and by comparing the
associated integral forces and moments. It is further important to evaluate
the performance in off-design conditions. For this reason the fairing
modification, which turned out to be the most promising candidate to
eliminate flow separation in the junction of the blade and the nacelle, is
investigated in comparison to the baseline geometry for further wind speeds,
namely U∞=8, 12 and 15 m s-1. These correspond to the
tip speed ratios of 7.48, 5 and 4, respectively. Since the pitch angle
is kept constant, the resulting pitch misalignments render somewhat
off-design “atmospheric” conditions. The two main questions to be answered
are whether the modified fairing geometry wastes performance at lower than
the design wind speed and whether an additional benefit can be obtained at
high wind speeds at which the overall tendency of flow separation increases.
The latter fact can be important with respect to atmospheric turbulence,
since gusts may cause local flow separation. If the amount of flow separation
can be reduced, an overall reduction of load fluctuations could be achieved.
Because unsteadiness is expected to increase with wind speed, the
computations at 12 and 15 m s-1 were continued unsteady from a
steady-state solution for two more revolutions. Time-averaging of the output
data was conducted for the last revolution. An overview on the effects of the
wind speed on the flow field can be gained from Fig. ,
in which a comparison is drawn between CaseT1.0-fairing and
CaseT1.0 based on the surface distributions of pressure and
streamlines, as well as based on the chord-wise velocity in an airfoil
section at z/R=0.2. At the lowest wind speed U∞=8 m s-1
corner separation has also almost vanished for the baseline geometry and very
similar pressure, streamline and velocity distributions are obtained in both
cases. For higher wind speeds the AoA increases, yielding a stronger
acceleration of the flow in the front part of the airfoil and accordingly in
very low surface pressures. As expected, the area of separation increases in
the chord-wise and radial direction. After detachment of the flow, the pressure
contours flatten out in conjunction with a strong effective de-cambering of
the airfoils. This is reflected in a significant recirculation area shown in
the velocity contours. Overall, CaseT1.0-fairing
significantly reduces the separated area for the high wind speed cases.
Particularly, the thickness of the separated wake is markedly reduced and the
accelerated regime in the front part of the airfoil is maintained. Both
result in a redirection of the airfoil wake, which consequently also turns
the aerodynamic force vector.
The resulting sectional thrust and driving loads of the blade are shown in
Figs. and .
Their integrated values for the resulting rotor thrust, driving force and torque (for
one blade) are summarized in Table . It must be
pointed out that for the lower wind speeds (U∞=8 and 10 m s-1)
an independent integration of each entire curve was not possible, since the
effect of the fairing on the overall performance is very small. The latter
fact is not surprising when keeping in mind that the flat-back blade offers
only little room for improvement compared to the massively separated root
sections of conventional blades. The problem is that, particularly for torque,
the smallest numerical uncertainties in the prediction of the forces in the
outer part of the rotor can outweigh the small improvements obtained in the
inner sections. Although the results shown in
Figs. and imply a very small
influence of the grid on the solution, it must be remembered from
Sect. that the two cases compared here cannot use exactly
the same grids due to topological reasons. Therefore, influences of the grid
cannot be eliminated completely. Nevertheless, to examine the
influence of the inner portion on the overall performance, each curve was
integrated separately only up to r/R≤0.35. The result was then
superposed in both cases by the same value calculated from the baseline
configuration for r/R>0.35. For the high wind speed cases U∞=12
and
15 m s-1 each curve was independently integrated over the whole
radius.
Influence of different wind speeds on the sectional thrust force.
CaseT1.0 (solid), CaseT1.0-fairing
(dashed).
Integral blade forces and torque for CaseT1.0 and
CaseT1.0-fairing at different wind speeds.
Thrust force (kN)
Wind speed (m s-1)
CaseT1.0
CaseT1.0-fairing
8
16.442
16.448 (+0.040 %)
10
23.187
23.212 (+0.108 %)
12
28.721
28.850 (+0.448 %)
15
32.878
33.113 (+0.714 %)
Driving force (kN)
Wind speed (m s-1)
CaseT1.0
CaseT1.0-fairing
8
1.624
1.628 (+0.202 %)
10
4.128
4.142 (+0.351 %)
12
6.936
7.029 (+1.336 %)
15
10.637
10.838 (+1.891 %)
Torque (kNm)
Wind speed (m s-1)
CaseT1.0
CaseT1.0-fairing
8
20.309
20.326 (+0.082 %)
10
50.873
50.923 (+0.099 %)
12
84.387
84.833 (+0.528 %)
15
127.007
127.693 (+0.540 %)
At the lowest wind speed U∞=8 m s-1 the phenomenological
impression made before is confirmed in the forces and integral quantities,
which are almost identical in both cases. Hence, the first question of whether
a performance degradation of the fairing is present at low wind speeds can be
negated. For the design wind speed U∞=10 m s-1 the local
improvement of the aerodynamics discussed in the previous section is
estimated to evoke a very small overall improvement of the extracted power by
around 0.1 %. When increasing the wind speed, the relative improvements
compared to the baseline configuration become more pronounced. In particular,
a rise of the driving force can be observed, which can be related to the
relative decrease in the pressure drag caused by the separated airfoil wake.
For the largest wind speed this means an overall power gain of 0.54 %.
To summarize these findings it can be stated that it is still important to
reduce the stall tendency of wind turbine blades in the inboard sections,
even if it might not be a severe problem at the design point of operation,
since at higher wind speeds and pitch misalignment flow separation will
always expand from the root in the outward direction. Therefore, the smaller the
triggering flow separation near the root, the less the mass of
separated flow that has to be transported outwards by the centrifugal pumping
mechanism, which means that “clean” aerodynamic behavior can be maintained
in the outer part of the rotor. With respect to situations of very high
atmospheric turbulence levels, in which such temporal pitch misalignments cannot
be avoided, an overall performance improvement can be expected in conjunction
with a reduction of load fluctuations.